In the Supplementary Information, we will report the medians of the posterior distributions, but both the medians and the means are shown in this document.

The credible intervals used are 95% CI.

In the function 'mcmc_intervals':

1 Model M0

1.1 Main parameters

1.1.1 Standard deviations

1.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.270 0.210 5.840 6.631
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148
\(\sigma_{S}\) 0.387 0.259 0.159 1.079
\(\sigma_{B}\) 0.045 0.007 0.032 0.061
\(\sigma\) 0.351 0.001 0.348 0.354

1.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.278 0.210 5.840 6.631
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148
\(\sigma_{S}\) 0.318 0.259 0.159 1.079
\(\sigma_{B}\) 0.044 0.007 0.032 0.061
\(\sigma\) 0.351 0.001 0.348 0.354

1.1.1.3 Figs

1.1.2 Variances

1.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{S}\) 0.217 0.527 0.025 1.165
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}\) 0.124 0.001 0.121 0.126
\(\beta_{0}\) 6.270 0.210 5.840 6.631
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148

1.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{S}\) 0.101 0.527 0.025 1.165
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}\) 0.124 0.001 0.121 0.126
\(\beta_{0}\) 6.278 0.210 5.840 6.631
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148

1.1.2.3 Figs

In the Supplementary Information.

1.2 Site intercepts

1.2.1 Tables

1.2.1.1 Mean

Term Mean Std.error Conf.low Conf.high
\(S_{Asturias}\) 0.282 0.211 -0.075 0.716
\(S_{Bordeaux}\) 0.137 0.210 -0.229 0.564
\(S_{Caceres}\) 0.073 0.211 -0.292 0.504
\(S_{Madrid}\) -0.361 0.211 -0.729 0.067
\(S_{Portugal}\) -0.109 0.210 -0.469 0.322

1.2.1.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(S_{Asturias}\) 0.273 0.211 -0.075 0.716
\(S_{Bordeaux}\) 0.128 0.210 -0.229 0.564
\(S_{Caceres}\) 0.065 0.211 -0.292 0.504
\(S_{Madrid}\) -0.371 0.211 -0.729 0.067
\(S_{Portugal}\) -0.118 0.210 -0.469 0.322

1.2.2 Figs

1.2.2.1 MCMC intervals

1.2.2.2 Density ridges

In the Supplementary Information.

2 Model M1

2.1 Main parameters

2.1.1 Standard deviations

2.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.239 0.190 5.866 6.627
\(\beta_{age}\) 0.599 0.002 0.594 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.146
\(\sigma_{P}\) 0.126 0.020 0.095 0.171
\(\sigma_{G}\) 0.106 0.004 0.098 0.114
\(\sigma_{S}\) 0.396 0.247 0.169 1.016
\(\sigma_{B}\) 0.043 0.007 0.032 0.059
\(\sigma\) 0.312 0.001 0.309 0.314

2.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.240 0.190 5.866 6.627
\(\beta_{age}\) 0.599 0.002 0.594 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.146
\(\sigma_{P}\) 0.125 0.020 0.095 0.171
\(\sigma_{G}\) 0.105 0.004 0.098 0.114
\(\sigma_{S}\) 0.331 0.247 0.169 1.016
\(\sigma_{B}\) 0.043 0.007 0.032 0.059
\(\sigma\) 0.312 0.001 0.309 0.314

2.1.1.3 Figs

2.1.2 Variances

2.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{P}\) 0.016 0.005 0.009 0.029
\(\sigma^{2}_{G}\) 0.011 0.001 0.010 0.013
\(\sigma^{2}_{S}\) 0.218 0.540 0.028 1.032
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}\) 0.097 0.001 0.095 0.099
\(\beta_{0}\) 6.239 0.190 5.866 6.627
\(\beta_{age}\) 0.599 0.002 0.594 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.146

2.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{P}\) 0.016 0.005 0.009 0.029
\(\sigma^{2}_{G}\) 0.011 0.001 0.010 0.013
\(\sigma^{2}_{S}\) 0.110 0.540 0.028 1.032
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}\) 0.097 0.001 0.095 0.099
\(\beta_{0}\) 6.240 0.190 5.866 6.627
\(\beta_{age}\) 0.599 0.002 0.594 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.146

2.1.2.3 Figs

In the Supplementary Information.

2.2 Site intercepts

2.2.1 Tables

2.2.1.1 Mean

Term Mean Std.error Conf.low Conf.high
\(S_{Asturias}\) 0.304 0.189 -0.078 0.679
\(S_{Bordeaux}\) 0.156 0.190 -0.227 0.530
\(S_{Caceres}\) 0.043 0.190 -0.342 0.426
\(S_{Madrid}\) -0.373 0.190 -0.763 0.004
\(S_{Portugal}\) -0.095 0.190 -0.474 0.291

2.2.1.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(S_{Asturias}\) 0.302 0.189 -0.078 0.679
\(S_{Bordeaux}\) 0.154 0.190 -0.227 0.530
\(S_{Caceres}\) 0.041 0.190 -0.342 0.426
\(S_{Madrid}\) -0.373 0.190 -0.763 0.004
\(S_{Portugal}\) -0.095 0.190 -0.474 0.291

2.2.2 Figs

2.2.2.1 MCMC intervals

2.2.2.2 Density ridges

In the Supplementary Information.

2.3 Conditional effect of age

In the Supplementary Information.

2.4 Provenance intercepts

2.4.1 Table

2.4.1.1 Mean

Term Mean Std.error Conf.low Conf.high
\(P_{ALT}\) 0.094 0.043 0.011 0.182
\(P_{ARM}\) 0.125 0.044 0.039 0.213
\(P_{ARN}\) -0.088 0.036 -0.159 -0.017
\(P_{BAY}\) -0.142 0.035 -0.212 -0.074
\(P_{BON}\) -0.044 0.041 -0.125 0.036
\(P_{CAR}\) -0.175 0.049 -0.269 -0.079
\(P_{CAS}\) 0.043 0.041 -0.036 0.125
\(P_{CEN}\) 0.015 0.043 -0.071 0.100
\(P_{COM}\) 0.068 0.055 -0.037 0.181
\(P_{CUE}\) -0.181 0.032 -0.243 -0.119
\(P_{HOU}\) 0.154 0.032 0.092 0.217
\(P_{LAM}\) 0.002 0.041 -0.080 0.081
\(P_{LEI}\) 0.035 0.032 -0.025 0.099
\(P_{MAD}\) 0.031 0.085 -0.136 0.198
\(P_{OLB}\) 0.040 0.033 -0.024 0.105
\(P_{OLO}\) 0.151 0.033 0.084 0.216
\(P_{ORI}\) -0.132 0.032 -0.197 -0.069
\(P_{PET}\) 0.115 0.034 0.051 0.181
\(P_{PIA}\) 0.083 0.036 0.012 0.151
\(P_{PIE}\) -0.094 0.043 -0.178 -0.010
\(P_{PUE}\) 0.067 0.043 -0.014 0.152
\(P_{SAL}\) -0.193 0.037 -0.265 -0.121
\(P_{SEG}\) 0.005 0.034 -0.062 0.073
\(P_{SIE}\) -0.007 0.044 -0.092 0.082
\(P_{STJ}\) 0.168 0.032 0.104 0.232
\(P_{TAM}\) -0.241 0.036 -0.311 -0.169
\(P_{VAL}\) -0.057 0.038 -0.134 0.017
\(P_{VER}\) 0.100 0.032 0.038 0.164

2.4.1.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(P_{ALT}\) 0.094 0.043 0.011 0.182
\(P_{ARM}\) 0.125 0.044 0.039 0.213
\(P_{ARN}\) -0.088 0.036 -0.159 -0.017
\(P_{BAY}\) -0.142 0.035 -0.212 -0.074
\(P_{BON}\) -0.044 0.041 -0.125 0.036
\(P_{CAR}\) -0.175 0.049 -0.269 -0.079
\(P_{CAS}\) 0.043 0.041 -0.036 0.125
\(P_{CEN}\) 0.015 0.043 -0.071 0.100
\(P_{COM}\) 0.068 0.055 -0.037 0.181
\(P_{CUE}\) -0.181 0.032 -0.243 -0.119
\(P_{HOU}\) 0.154 0.032 0.092 0.217
\(P_{LAM}\) 0.002 0.041 -0.080 0.081
\(P_{LEI}\) 0.035 0.032 -0.025 0.099
\(P_{MAD}\) 0.031 0.085 -0.136 0.198
\(P_{OLB}\) 0.040 0.033 -0.024 0.105
\(P_{OLO}\) 0.151 0.033 0.084 0.216
\(P_{ORI}\) -0.132 0.032 -0.197 -0.069
\(P_{PET}\) 0.115 0.034 0.051 0.181
\(P_{PIA}\) 0.083 0.036 0.012 0.151
\(P_{PIE}\) -0.094 0.043 -0.178 -0.010
\(P_{PUE}\) 0.067 0.043 -0.014 0.152
\(P_{SAL}\) -0.193 0.037 -0.265 -0.121
\(P_{SEG}\) 0.005 0.034 -0.062 0.073
\(P_{SIE}\) -0.007 0.044 -0.092 0.082
\(P_{STJ}\) 0.168 0.032 0.104 0.232
\(P_{TAM}\) -0.241 0.036 -0.311 -0.169
\(P_{VAL}\) -0.057 0.038 -0.134 0.017
\(P_{VER}\) 0.100 0.032 0.038 0.164

2.4.2 Figs

2.4.2.1 Density Ridges

3 Model M2

3.1 Main parameters

3.1.1 Standard deviations

3.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.227 0.226 5.777 6.686
\(\beta_{age}\) 0.598 0.002 0.593 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.145
\(\sigma_{P}\) 0.120 0.020 0.087 0.164
\(\sigma_{G}\) 0.106 0.004 0.098 0.115
\(\sigma_{Inter}\) 0.070 0.007 0.057 0.084
\(\sigma_{S}\) 0.431 0.288 0.174 1.238
\(\sigma_{B}\) 0.043 0.007 0.031 0.058
\(\sigma\) 0.309 0.001 0.306 0.311

3.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.229 0.226 5.777 6.686
\(\beta_{age}\) 0.598 0.002 0.593 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.145
\(\sigma_{P}\) 0.118 0.020 0.087 0.164
\(\sigma_{G}\) 0.106 0.004 0.098 0.115
\(\sigma_{Inter}\) 0.069 0.007 0.057 0.084
\(\sigma_{S}\) 0.350 0.288 0.174 1.238
\(\sigma_{B}\) 0.042 0.007 0.031 0.058
\(\sigma\) 0.309 0.001 0.306 0.311

3.1.1.3 Figs

3.1.2 Variances

3.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{P}\) 0.015 0.005 0.008 0.027
\(\sigma^{2}_{G}\) 0.011 0.001 0.010 0.013
\(\sigma^{2}_{Inter}\) 0.005 0.001 0.003 0.007
\(\sigma^{2}_{S}\) 0.269 0.584 0.030 1.532
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}\) 0.095 0.001 0.094 0.097
\(\beta_{0}\) 6.227 0.226 5.777 6.686
\(\beta_{age}\) 0.598 0.002 0.593 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.145

3.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{P}\) 0.014 0.005 0.008 0.027
\(\sigma^{2}_{G}\) 0.011 0.001 0.010 0.013
\(\sigma^{2}_{Inter}\) 0.005 0.001 0.003 0.007
\(\sigma^{2}_{S}\) 0.123 0.584 0.030 1.532
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}\) 0.095 0.001 0.094 0.097
\(\beta_{0}\) 6.229 0.226 5.777 6.686
\(\beta_{age}\) 0.598 0.002 0.593 0.603
\(\beta_{age2}\) -0.150 0.002 -0.155 -0.145

3.1.2.3 Figs

In the Supplementary Information.

3.2 Site intercepts

3.2.1 Tables

3.2.1.1 Mean

Parameter Mean SD InfCI SupCI
\(S_{Asturias}\) 0.319 0.225 -0.134 0.770
\(S_{Bordeaux}\) 0.154 0.224 -0.304 0.597
\(S_{Caceres}\) 0.034 0.226 -0.428 0.488
\(S_{Madrid}\) -0.380 0.225 -0.838 0.062
\(S_{Portugal}\) -0.087 0.225 -0.541 0.360

3.2.1.2 Median

Parameter Median SD InfCI SupCI
\(S_{Asturias}\) 0.314 0.225 -0.134 0.770
\(S_{Bordeaux}\) 0.148 0.224 -0.304 0.597
\(S_{Caceres}\) 0.031 0.226 -0.428 0.488
\(S_{Madrid}\) -0.382 0.225 -0.838 0.062
\(S_{Portugal}\) -0.090 0.225 -0.541 0.360

3.2.2 Figs

3.2.2.1 MCMC intervals

3.3 Provenance intercepts

3.3.1 ALL

3.3.2 Portugal

3.3.3 Caceres

3.3.4 Madrid

3.3.5 Bordeaux

3.3.6 Asturias

3.3.7 Merging the plots

In the Supplementary Information.

4 MODEL M7

4.1 Main parameters

4.1.1 Standard deviations

4.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.315 0.345 5.624 7.068
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147
\(\sigma_{B}\) 0.044 0.007 0.032 0.061
\(\sigma_{g_{j}}\) 0.190 0.098 0.089 0.442
\(\sigma_{S}\) 0.491 0.329 0.190 1.388
\(\sigma_{\beta_{max.temp,s}}\) 0.034 0.020 0.009 0.083
\(\sigma_{\beta_{min.pre,s}}\) 0.034 0.021 0.009 0.085
\(\sigma_{\beta_{gPEA,s}}\) 0.158 0.083 0.072 0.369
\(\sigma\) 0.321 0.001 0.318 0.323

4.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.310 0.345 5.624 7.068
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147
\(\sigma_{B}\) 0.044 0.007 0.032 0.061
\(\sigma_{g_{j}}\) 0.165 0.098 0.089 0.442
\(\sigma_{S}\) 0.396 0.329 0.190 1.388
\(\sigma_{\beta_{max.temp,s}}\) 0.030 0.020 0.009 0.083
\(\sigma_{\beta_{min.pre,s}}\) 0.030 0.021 0.009 0.085
\(\sigma_{\beta_{gPEA,s}}\) 0.138 0.083 0.072 0.369
\(\sigma\) 0.321 0.001 0.318 0.323

4.1.1.3 Figs

4.1.2 Variances

4.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}_{g_{j}}\) 0.046 0.076 0.008 0.195
\(\sigma^{2}_{S}\) 0.349 0.837 0.036 1.926
\(\sigma^{2}_{\beta_{max.temp,s}}\) 0.002 0.004 0.000 0.007
\(\sigma^{2}_{\beta_{min.pre,s}}\) 0.002 0.004 0.000 0.007
\(\sigma^{2}_{\beta_{gPEA,s}}\) 0.032 0.055 0.005 0.136
\(\sigma^{2}\) 0.103 0.001 0.101 0.104
\(\beta_{0}\) 6.315 0.345 5.624 7.068
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147

4.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}_{g_{j}}\) 0.027 0.076 0.008 0.195
\(\sigma^{2}_{S}\) 0.157 0.837 0.036 1.926
\(\sigma^{2}_{\beta_{max.temp,s}}\) 0.001 0.004 0.000 0.007
\(\sigma^{2}_{\beta_{min.pre,s}}\) 0.001 0.004 0.000 0.007
\(\sigma^{2}_{\beta_{gPEA,s}}\) 0.019 0.055 0.005 0.136
\(\sigma^{2}\) 0.103 0.001 0.101 0.104
\(\beta_{0}\) 6.310 0.345 5.624 7.068
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147

4.1.2.3 Figs

In the Supplementary Information.

4.2 Gene pool intercepts

4.2.1 Table

Term Mean Std.error Conf.low Conf.high
\(g_{NA}\) -0.218 0.090 -0.391 -0.044
\(g_{C}\) 0.029 0.090 -0.142 0.206
\(g_{CS}\) -0.080 0.089 -0.253 0.099
\(g_{FA}\) 0.164 0.090 -0.006 0.344
\(g_{IA}\) 0.094 0.090 -0.080 0.274
\(g_{SES}\) 0.032 0.090 -0.140 0.207

4.2.2 Figs

4.2.2.1 MCMC intervals

4.2.2.2 Density ridges

4.3 Maximum temperature of the warmest month

4.3.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{max.temp,Asturias}\) -0.006 0.005 -0.016 0.004
\(\beta_{max.temp,Bordeaux}\) -0.007 0.006 -0.019 0.005
\(\beta_{max.temp,Caceres}\) 0.014 0.019 -0.020 0.055
\(\beta_{max.temp,Madrid}\) 0.050 0.019 0.013 0.087
\(\beta_{max.temp,Portugal}\) 0.004 0.005 -0.005 0.014

4.3.2 Figs

4.4 Minimum precipitation of the driest month

4.4.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{min.pre,Asturias}\) -0.001 0.006 -0.013 0.011
\(\beta_{min.pre,Bordeaux}\) 0.010 0.007 -0.005 0.024
\(\beta_{min.pre,Caceres}\) 0.028 0.019 -0.005 0.070
\(\beta_{min.pre,Madrid}\) 0.049 0.019 0.012 0.084
\(\beta_{min.pre,Portugal}\) 0.009 0.006 -0.002 0.021

4.4.2 Figs

4.5 gPEAs

= global Positive effect alleles

4.5.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{gPEA,Asturias}\) 0.082 0.003 0.076 0.088
\(\beta_{gPEA,Bordeaux}\) 0.091 0.004 0.082 0.100
\(\beta_{gPEA,Caceres}\) 0.115 0.019 0.079 0.153
\(\beta_{gPEA,Madrid}\) 0.127 0.011 0.105 0.149
\(\beta_{gPEA,Portugal}\) 0.107 0.003 0.100 0.113

4.5.2 Figs

5 MODEL M8

5.1 Main parameters

5.1.1 Standard deviations

5.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.345 0.366 5.602 7.106
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147
\(\sigma_{B}\) 0.043 0.007 0.031 0.058
\(\sigma_{g_{j}}\) 0.207 0.102 0.099 0.473
\(\sigma_{S}\) 0.547 0.388 0.202 1.538
\(\sigma_{\beta_{max.temp,s}}\) 0.062 0.029 0.028 0.139
\(\sigma_{\beta_{min.pre,s}}\) 0.049 0.025 0.021 0.117
\(\sigma_{\beta_{rPEA,s}}\) 0.209 0.108 0.099 0.491
\(\sigma\) 0.318 0.001 0.315 0.320

5.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.337 0.366 5.602 7.106
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147
\(\sigma_{B}\) 0.042 0.007 0.031 0.058
\(\sigma_{g_{j}}\) 0.179 0.102 0.099 0.473
\(\sigma_{S}\) 0.436 0.388 0.202 1.538
\(\sigma_{\beta_{max.temp,s}}\) 0.056 0.029 0.028 0.139
\(\sigma_{\beta_{min.pre,s}}\) 0.043 0.025 0.021 0.117
\(\sigma_{\beta_{rPEA,s}}\) 0.180 0.108 0.099 0.491
\(\sigma\) 0.318 0.001 0.315 0.320

5.1.1.3 Figs

5.1.2 Variances

5.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}_{g_{j}}\) 0.053 0.075 0.010 0.224
\(\sigma^{2}_{S}\) 0.449 1.195 0.041 2.366
\(\sigma^{2}_{\beta_{max.temp,s}}\) 0.005 0.006 0.001 0.019
\(\sigma^{2}_{\beta_{min.pre,s}}\) 0.003 0.004 0.000 0.014
\(\sigma^{2}_{\beta_{rPEA,s}}\) 0.055 0.085 0.010 0.241
\(\sigma^{2}\) 0.101 0.001 0.099 0.103
\(\beta_{0}\) 6.345 0.366 5.602 7.106
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147

5.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}_{g_{j}}\) 0.032 0.075 0.010 0.224
\(\sigma^{2}_{S}\) 0.190 1.195 0.041 2.366
\(\sigma^{2}_{\beta_{max.temp,s}}\) 0.003 0.006 0.001 0.019
\(\sigma^{2}_{\beta_{min.pre,s}}\) 0.002 0.004 0.000 0.014
\(\sigma^{2}_{\beta_{rPEA,s}}\) 0.032 0.085 0.010 0.241
\(\sigma^{2}\) 0.101 0.001 0.099 0.103
\(\beta_{0}\) 6.337 0.366 5.602 7.106
\(\beta_{age}\) 0.600 0.003 0.595 0.605
\(\beta_{age2}\) -0.151 0.002 -0.156 -0.147

5.1.2.3 Figs

In the Supplementary Information.

5.2 Gene pool intercepts

5.2.1 Table

Term Mean Std.error Conf.low Conf.high
\(g_{NA}\) -0.239 0.097 -0.425 -0.048
\(g_{C}\) 0.056 0.097 -0.128 0.248
\(g_{CS}\) -0.081 0.097 -0.265 0.110
\(g_{FA}\) 0.168 0.097 -0.018 0.359
\(g_{IA}\) 0.120 0.097 -0.065 0.310
\(g_{SES}\) 0.004 0.097 -0.179 0.199

5.2.2 Figs

5.2.2.1 MCMC intervals

5.2.2.2 Density ridges

5.3 Maximum temperature of the warmest month

5.3.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{max.temp,Asturias}\) 0.000 0.005 -0.010 0.010
\(\beta_{max.temp,Bordeaux}\) -0.005 0.007 -0.018 0.008
\(\beta_{max.temp,Caceres}\) 0.040 0.023 -0.002 0.086
\(\beta_{max.temp,Madrid}\) 0.094 0.016 0.062 0.127
\(\beta_{max.temp,Portugal}\) 0.008 0.005 -0.001 0.018

5.3.2 Figs

5.4 Minimum precipitation of the driest month

5.4.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{min.pre,Asturias}\) -0.014 0.006 -0.025 -0.002
\(\beta_{min.pre,Bordeaux}\) 0.023 0.007 0.009 0.037
\(\beta_{min.pre,Caceres}\) 0.029 0.021 -0.010 0.072
\(\beta_{min.pre,Madrid}\) 0.060 0.016 0.030 0.091
\(\beta_{min.pre,Portugal}\) -0.008 0.006 -0.019 0.003

5.4.2 Figs

5.5 rPEAs

5.5.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{rPEA,Asturias}\) 0.102 0.004 0.095 0.110
\(\beta_{rPEA,Bordeaux}\) 0.109 0.005 0.100 0.119
\(\beta_{rPEA,Caceres}\) 0.156 0.020 0.117 0.196
\(\beta_{rPEA,Madrid}\) 0.200 0.012 0.178 0.224
\(\beta_{rPEA,Portugal}\) 0.127 0.004 0.120 0.134

5.5.2 Figs

6 Model M9

6.1 Main parameters

6.1.1 Standard deviations

6.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.229 0.217 5.802 6.647
\(\beta_{age}\) 0.602 0.003 0.597 0.608
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148
\(\sigma_{g_{j}}\) 0.190 0.101 0.089 0.446
\(\sigma_{S}\) 0.394 0.248 0.163 1.010
\(\sigma_{B}\) 0.045 0.007 0.033 0.061
\(\sigma\) 0.335 0.001 0.332 0.337

6.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.230 0.217 5.802 6.647
\(\beta_{age}\) 0.602 0.003 0.597 0.608
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148
\(\sigma_{g_{j}}\) 0.165 0.101 0.089 0.446
\(\sigma_{S}\) 0.329 0.248 0.163 1.010
\(\sigma_{B}\) 0.044 0.007 0.033 0.061
\(\sigma\) 0.335 0.001 0.332 0.337

6.1.1.3 Figs

6.1.2 Variances

6.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{g_{j}}\) 0.046 0.083 0.008 0.199
\(\sigma^{2}_{S}\) 0.217 0.622 0.027 1.019
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}\) 0.112 0.001 0.110 0.114
\(\beta_{0}\) 6.229 0.217 5.802 6.647
\(\beta_{age}\) 0.602 0.003 0.597 0.608
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148

6.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{g_{j}}\) 0.027 0.083 0.008 0.199
\(\sigma^{2}_{S}\) 0.108 0.622 0.027 1.019
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}\) 0.112 0.001 0.110 0.114
\(\beta_{0}\) 6.230 0.217 5.802 6.647
\(\beta_{age}\) 0.602 0.003 0.597 0.608
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148

6.1.2.3 Figs

6.2 Gene pool intercepts

6.2.1 Table

6.2.1.1 Mean

Term Mean Std.error Conf.low Conf.high
\(g_{NA}\) -0.206 0.089 -0.374 -0.018
\(g_{C}\) 0.054 0.089 -0.108 0.242
\(g_{CS}\) -0.074 0.088 -0.236 0.113
\(g_{FA}\) 0.178 0.088 0.014 0.366
\(g_{IA}\) 0.087 0.088 -0.080 0.274
\(g_{SES}\) -0.013 0.089 -0.178 0.175

6.2.1.2 Median

Term Mean Std.error Conf.low Conf.high
\(g_{NA}\) -0.207 0.089 -0.374 -0.018
\(g_{C}\) 0.052 0.089 -0.108 0.242
\(g_{CS}\) -0.076 0.088 -0.236 0.113
\(g_{FA}\) 0.176 0.088 0.014 0.366
\(g_{IA}\) 0.084 0.088 -0.080 0.274
\(g_{SES}\) -0.014 0.089 -0.178 0.175

6.2.2 Figs

7 MODEL M10

7.1 Main parameters

7.1.1 Standard deviations

7.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.222 0.456 5.194 7.075
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148
\(\sigma_{B}\) 0.044 0.007 0.032 0.060
\(\sigma_{S}\) 0.555 0.457 0.190 1.734
\(\sigma_{\beta_{max.temp,s}}\) 0.083 0.040 0.039 0.186
\(\sigma_{\beta_{min.pre,s}}\) 0.091 0.047 0.041 0.202
\(\sigma\) 0.337 0.001 0.334 0.339

7.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.239 0.456 5.194 7.075
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148
\(\sigma_{B}\) 0.043 0.007 0.032 0.060
\(\sigma_{S}\) 0.428 0.457 0.190 1.734
\(\sigma_{\beta_{max.temp,s}}\) 0.073 0.040 0.039 0.186
\(\sigma_{\beta_{min.pre,s}}\) 0.080 0.047 0.041 0.202
\(\sigma\) 0.337 0.001 0.334 0.339

7.1.1.3 Figs

7.1.2 Variances

7.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}_{S}\) 0.517 1.789 0.036 3.006
\(\sigma^{2}_{\beta_{max.temp,s}}\) 0.009 0.011 0.002 0.035
\(\sigma^{2}_{\beta_{min.pre,s}}\) 0.010 0.018 0.002 0.041
\(\sigma^{2}\) 0.113 0.001 0.111 0.115
\(\beta_{0}\) 6.222 0.456 5.194 7.075
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148

7.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}_{S}\) 0.183 1.789 0.036 3.006
\(\sigma^{2}_{\beta_{max.temp,s}}\) 0.005 0.011 0.002 0.035
\(\sigma^{2}_{\beta_{min.pre,s}}\) 0.006 0.018 0.002 0.041
\(\sigma^{2}\) 0.113 0.001 0.111 0.115
\(\beta_{0}\) 6.239 0.456 5.194 7.075
\(\beta_{age}\) 0.602 0.003 0.597 0.607
\(\beta_{age2}\) -0.153 0.003 -0.158 -0.148

7.1.2.3 Figs

In the Supplementary Information.

7.2 Maximum temperature of the warmest month

7.2.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{max.temp,Asturias}\) -0.068 0.005 -0.077 -0.059
\(\beta_{max.temp,Bordeaux}\) -0.071 0.006 -0.083 -0.059
\(\beta_{max.temp,Caceres}\) -0.048 0.022 -0.091 -0.005
\(\beta_{max.temp,Madrid}\) 0.003 0.016 -0.029 0.035
\(\beta_{max.temp,Portugal}\) -0.062 0.004 -0.071 -0.053

7.2.2 Figs

7.3 Minimum precipitation of the driest month

7.3.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{min.pre,Asturias}\) 0.038 0.005 0.029 0.047
\(\beta_{min.pre,Bordeaux}\) 0.052 0.006 0.040 0.065
\(\beta_{min.pre,Caceres}\) 0.062 0.021 0.022 0.104
\(\beta_{min.pre,Madrid}\) 0.093 0.016 0.063 0.125
\(\beta_{min.pre,Portugal}\) 0.045 0.004 0.036 0.053

7.3.2 Figs

7.3.3 Both

8 Model M11

8.1 Main parameters

8.1.1 Standard deviations

8.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.452 0.677 5.164 7.956
\(\beta_{age}\) 0.600 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146
\(\sigma_{B}\) 0.044 0.007 0.032 0.060
\(\sigma_{S}\) 0.715 0.615 0.196 2.366
\(\sigma_{\beta_{gPEA,s}}\) 0.132 0.064 0.064 0.292
\(\sigma\) 0.339 0.001 0.336 0.342

8.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.374 0.677 5.164 7.956
\(\beta_{age}\) 0.600 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146
\(\sigma_{B}\) 0.044 0.007 0.032 0.060
\(\sigma_{S}\) 0.515 0.615 0.196 2.366
\(\sigma_{\beta_{gPEA,s}}\) 0.116 0.064 0.064 0.292
\(\sigma\) 0.339 0.001 0.336 0.342

8.1.1.3 Figs

8.1.2 Variances

8.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}_{S}\) 0.890 2.482 0.038 5.597
\(\sigma^{2}_{\beta_{gPEA,s}}\) 0.021 0.031 0.004 0.085
\(\sigma^{2}\) 0.115 0.001 0.113 0.117
\(\beta_{0}\) 6.452 0.677 5.164 7.956
\(\beta_{age}\) 0.600 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146

8.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.004
\(\sigma^{2}_{S}\) 0.265 2.482 0.038 5.597
\(\sigma^{2}_{\beta_{gPEA,s}}\) 0.013 0.031 0.004 0.085
\(\sigma^{2}\) 0.115 0.001 0.113 0.117
\(\beta_{0}\) 6.374 0.677 5.164 7.956
\(\beta_{age}\) 0.600 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146

8.1.2.3 Figs

In the Supplementary Information.

8.2 gPEAs

= global Positive effect alleles

8.2.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{gPEA,Asturias}\) 0.079 0.003 0.073 0.086
\(\beta_{gPEA,Bordeaux}\) 0.099 0.005 0.090 0.108
\(\beta_{gPEA,Caceres}\) 0.091 0.019 0.054 0.127
\(\beta_{gPEA,Madrid}\) 0.109 0.012 0.085 0.133
\(\beta_{gPEA,Portugal}\) 0.101 0.003 0.095 0.108

8.2.2 Figs

9 Model M12

9.1 Main parameters

9.1.1 Standard deviations

9.1.1.1 Mean

Parameter Mean SD InfCI SupCI
\(\beta_{0}\) 6.612 0.532 5.620 7.714
\(\beta_{age}\) 0.599 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146
\(\sigma_{B}\) 0.043 0.007 0.031 0.058
\(\sigma_{S}\) 0.738 0.579 0.205 2.158
\(\sigma_{\beta_{rPEA,s}}\) 0.184 0.097 0.088 0.421
\(\sigma\) 0.335 0.001 0.332 0.338

9.1.1.2 Median

Parameter Median SD InfCI SupCI
\(\beta_{0}\) 6.556 0.532 5.620 7.714
\(\beta_{age}\) 0.599 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146
\(\sigma_{B}\) 0.042 0.007 0.031 0.058
\(\sigma_{S}\) 0.576 0.579 0.205 2.158
\(\sigma_{\beta_{rPEA,s}}\) 0.160 0.097 0.088 0.421
\(\sigma\) 0.335 0.001 0.332 0.338

9.1.1.3 Figs

9.1.2 Variances

9.1.2.1 Mean

Parameter Mean SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}_{S}\) 0.880 2.743 0.042 4.656
\(\sigma^{2}_{\beta_{rPEA,s}}\) 0.043 0.083 0.008 0.177
\(\sigma^{2}\) 0.112 0.001 0.110 0.114
\(\beta_{0}\) 6.612 0.532 5.620 7.714
\(\beta_{age}\) 0.599 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146

9.1.2.2 Median

In the Supplementary Information.

Parameter Median SD InfCI SupCI
\(\sigma^{2}_{B}\) 0.002 0.001 0.001 0.003
\(\sigma^{2}_{S}\) 0.332 2.743 0.042 4.656
\(\sigma^{2}_{\beta_{rPEA,s}}\) 0.026 0.083 0.008 0.177
\(\sigma^{2}\) 0.112 0.001 0.110 0.114
\(\beta_{0}\) 6.556 0.532 5.620 7.714
\(\beta_{age}\) 0.599 0.003 0.594 0.605
\(\beta_{age2}\) -0.151 0.003 -0.156 -0.146

9.1.2.3 Figs

In the Supplementary Information.

9.2 rPEAs

= region-specific Positive effect alleles

9.2.1 Table

Term Mean Std.error Conf.low Conf.high
\(\beta_{rPEA,Asturias}\) 0.109 0.004 0.101 0.116
\(\beta_{rPEA,Bordeaux}\) 0.093 0.005 0.084 0.102
\(\beta_{rPEA,Caceres}\) 0.138 0.020 0.100 0.178
\(\beta_{rPEA,Madrid}\) 0.179 0.012 0.156 0.203
\(\beta_{rPEA,Portugal}\) 0.132 0.004 0.125 0.139

9.2.2 Figs